Controllability of Coarsely Measured Networked Linear Dynamical Systems (Extended Version)

• URL: http://arxiv.org/abs/2206.10569v1
• Date: Tue, 21 Jun 2022 17:50:09 GMT
• Title: Controllability of Coarsely Measured Networked Linear Dynamical Systems (Extended Version)
• Authors: Nafiseh Ghoroghchian and Rajasekhar Anguluri and Gautam Dasarathy and Stark C. Draper
• Abstract summary: We consider the controllability of large-scale linear networked dynamical systems when complete knowledge of network structure is unavailable. We provide conditions under which average controllability of the fine-scale system can be well approximated by average controllability of the (synthesized, reduced-order) coarse-scale system.
• Score: 19.303541162361746
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider the controllability of large-scale linear networked dynamical systems when complete knowledge of network structure is unavailable and knowledge is limited to coarse summaries. We provide conditions under which average controllability of the fine-scale system can be well approximated by average controllability of the (synthesized, reduced-order) coarse-scale system. To this end, we require knowledge of some inherent parametric structure of the fine-scale network that makes this type of approximation possible. Therefore, we assume that the underlying fine-scale network is generated by the stochastic block model (SBM) -- often studied in community detection. We then provide an algorithm that directly estimates the average controllability of the fine-scale system using a coarse summary of SBM. Our analysis indicates the necessity of underlying structure (e.g., in-built communities) to be able to quantify accurately the controllability from coarsely characterized networked dynamics. We also compare our method to that of the reduced-order method and highlight the regimes where both can outperform each other. Finally, we provide simulations to confirm our theoretical results for different scalings of network size and density, and the parameter that captures how much community-structure is retained in the coarse summary.

Related papers

• Predicting Instability in Complex Oscillator Networks: Limitations and Potentials of Network Measures and Machine Learning [0.0]
  We collect 46 relevant network measures and find that no small subset can reliably predict stability. The performance of GNNs can only be matched by combining all network measures and nodewise machine learning. This suggests that correlations of network measures and function may be misleading, and that GNNs capture the causal relationship between structure and stability substantially better.
  arXiv  Detail & Related papers  (2024-02-27T13:34:08Z)
• Optimization Guarantees of Unfolded ISTA and ADMM Networks With Smooth Soft-Thresholding [57.71603937699949]
  We study optimization guarantees, i.e., achieving near-zero training loss with the increase in the number of learning epochs. We show that the threshold on the number of training samples increases with the increase in the network width.
  arXiv  Detail & Related papers  (2023-09-12T13:03:47Z)
• Dense Hebbian neural networks: a replica symmetric picture of supervised learning [4.133728123207142]
  We consider dense, associative neural-networks trained by a teacher with supervision. We investigate their computational capabilities analytically, via statistical-mechanics of spin glasses, and numerically, via Monte Carlo simulations.
  arXiv  Detail & Related papers  (2022-11-25T13:37:47Z)
• Large-Scale Sequential Learning for Recommender and Engineering Systems [91.3755431537592]
  In this thesis, we focus on the design of an automatic algorithms that provide personalized ranking by adapting to the current conditions. For the former, we propose novel algorithm called SAROS that take into account both kinds of feedback for learning over the sequence of interactions. The proposed idea of taking into account the neighbour lines shows statistically significant results in comparison with the initial approach for faults detection in power grid.
  arXiv  Detail & Related papers  (2022-05-13T21:09:41Z)
• Systematic assessment of the quality of fit of the stochastic block model for empirical networks [0.0]
  We analyze the quality of fit of the block model (SBM) for 275 empirical networks spanning a wide range of domains and orders of size magnitude. We observe that the SBM is capable of providing an accurate description for the majority of networks considered, but falls short of saturating all modeling requirements.
  arXiv  Detail & Related papers  (2022-01-05T15:28:37Z)
• Sparsity in Partially Controllable Linear Systems [56.142264865866636]
  We study partially controllable linear dynamical systems specified by an underlying sparsity pattern. Our results characterize those state variables which are irrelevant for optimal control.
  arXiv  Detail & Related papers  (2021-10-12T16:41:47Z)
• KalmanNet: Neural Network Aided Kalman Filtering for Partially Known Dynamics [84.18625250574853]
  We present KalmanNet, a real-time state estimator that learns from data to carry out Kalman filtering under non-linear dynamics. We numerically demonstrate that KalmanNet overcomes nonlinearities and model mismatch, outperforming classic filtering methods.
  arXiv  Detail & Related papers  (2021-07-21T12:26:46Z)
• Formal Verification of Stochastic Systems with ReLU Neural Network Controllers [22.68044012584378]
  We address the problem of formal safety verification for cyber-physical systems equipped with ReLU neural network (NN) controllers. Our goal is to find the set of initial states from where, with a predetermined confidence, the system will not reach an unsafe configuration.
  arXiv  Detail & Related papers  (2021-03-08T23:53:13Z)
• Anomaly Detection on Attributed Networks via Contrastive Self-Supervised Learning [50.24174211654775]
  We present a novel contrastive self-supervised learning framework for anomaly detection on attributed networks. Our framework fully exploits the local information from network data by sampling a novel type of contrastive instance pair. A graph neural network-based contrastive learning model is proposed to learn informative embedding from high-dimensional attributes and local structure.
  arXiv  Detail & Related papers  (2021-02-27T03:17:20Z)
• Safety Verification of Neural Network Controlled Systems [0.0]
  We propose a system-level approach for verifying the safety of neural network controlled systems. We assume a generic model for the controller that can capture both simple and complex behaviours. We perform a reachability analysis that soundly approximates the reachable states of the overall system.
  arXiv  Detail & Related papers  (2020-11-10T15:26:38Z)
• Network Diffusions via Neural Mean-Field Dynamics [52.091487866968286]
  We propose a novel learning framework for inference and estimation problems of diffusion on networks. Our framework is derived from the Mori-Zwanzig formalism to obtain an exact evolution of the node infection probabilities. Our approach is versatile and robust to variations of the underlying diffusion network models.
  arXiv  Detail & Related papers  (2020-06-16T18:45:20Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.